|If it took 3 days for the Apollo astronauts to travel to the Moon, what was their average speed in units of km per hour, km per second and miles per hour?|
|Question Date: 2019-11-18|
The average distance between the earth and the moon is 238,900 mi. We'll assume for this problem that the astronauts flew in a straight line from the earth to the moon (though in reality they travelled in an arc). To do this problem, we need to make a few conversions. Let's take a look:
1 mile = 1.61 km
1 day = 24 hours
1 hour = 60 mins
1 min = 60 seconds
In each step of our conversions, we have to make the units cancel so that we get our final desired units. So, if you want the speed in km/hr, you have to convert miles to kilometers and days to hours. I've done this in the calculations below, but you should double check that the undesired units cancel out.
Let's start with the easy one:miles per hour:
The astronauts travelled 238,900 mi in three days.
(238,900 mi/3 days)*(1 day/24 hours)= 238,900 mi/(3*24 hours)... I'll let you do the math.
Next, speed in km/hr.
(238,900 mi/3 days)*(1 day/24 hours)*(1.61 km/1 mi) = (238,900*1.61 km)/(3*24 hours)
Finally, speed in km/s.
(238,900 mi/3 days)*(1 day/24 hours)*(1 hour/60 minutes)*(1 min/60 sec)*(1.61 km/1 mi) = (238,900*1.61 km)/(3*24*60*60 sec)
For this question, we can start with the distance from the Earth to the moon, which is 238,900 miles. To convert miles to km, we can use the fact that 1 mile is about 1.61 km. Then, to find the speeds you mentioned, we take the total distance from the Earth to the moon in km, and divide by the number of hours in 3 days. We also divide the distance by the number of seconds in 3 days, which we can calculate by multiplying the number of hours by 60 (there are 60 minutes in 1 hour) to get the number of minutes in 3 days, and then multiplying the number of minutes by 60 to get the number of seconds in 3 days. These two calculations will give us the average speed in km per hour and km per second.
We can also then divide the distance in miles by the number of hours to get the average speed in miles per hour. All average speed problems can be solved like this - by finding the total distance traveled, dividing the distance by the total time the trip took, and paying attention to units.
The distance from Earth to the moon is 238,900 miles. 1 mile is equal to approximately 1.6 km, meaning the moon is 382,200 km away.
Now, if the trip took three days, that's equivalent to 72 hours. To find the average speed in km/hr, divide 382200 by 72 to get the speed in km/hr. To get that speed per second, you have to divide your earlier calculated value by 3600 (number of seconds in an hour). Finally, if you want it in miles per hour, divide the earlier distance in miles by 72 hours. Hope that helps!
"Apollo 11 was programmed to travel 240,000 miles in 76 hours before entering into a lunar orbit on July 19. ",
flight plan for Apollo 11.
240,000 miles / 76 hr = 316 miles/hr
1 mile = 1.6 km
1 km = 0.6 mile
1 hr = 3600 seconds
You can figure out the rest!
The distance from the earth to the moon is 238,900 miles, so if the astronauts were traveling for 72 hours, their average speed was 238,900 miles/72 hours = 3318.06 miles per hour.
We can convert this to km per hour as follows:
289300 miles/72 hours * 1.60934 km/mile = 5339.88 km/hour.
We can convert this to km per second:
289300 miles/72 hours * 1.60934 km/mile* 1 hour/3600 seconds = 1.48 km/second.
To get average speed, we divide the total distance by the total time it takes to travel that distance.
If we assume the distance to the moon is 238,900 miles then we divide by 72 hours to get roughly 3318 mph.
To get this in km per hr, we have to convert miles to kilometers. There are roughly 1.6 km per mile, so we multiply 238,900 mi/hr *(1.6 km/mi) = 382240 km/hr.
If we want km per second, we have to multiply the 72 hours by 60 to get it in terms of minutes, then 60 again to get it in terms of seconds. So we end up with 382240 km/hr * (60 min/hr) * (60 sec/min) = 1376064000 km/s
Specifically for Apollo 11 (the first moon landing), they traveled about 386,000 km in 76 hours (a bit over 3 days) before entering lunar orbit. This equates to an average speed of 5,082 km/hr, or 1.41 km/s or 3,157 miles/hr.
This metric can be variable for other missions however, especially given the distance between the moon and earth is not constant. The moon can be as close as 363,104 km to the earth and as far as 405,696 km.
This is a simple problem of applying the basic distance/rate/time relationship and dimensional analysis.
The relationship is distance = rate x time, written with variables as d = r x t, which can be rearranged to calculate rate as r = d/t. This rate can be calculated in km/hr, km/s, and mi/hr.
Once the rate is found in one set of units, it can be converted to others using ratios of the form (X of unit you want) / (Y of unit you have). For example, the conversion factor for inches to centimeters is (2.54 cm) / (1 inch). Thus, converting 4 inches to centimeters is accomplished by:
(4 in) * (2.54 cm) / (1 in) = 10.16 cm.
Using the quantities of the problem, the rate of interest is r = (distance to the Moon) / (time to reach the Moon). The question asks first for rate in km per hour, given by r (km/hr) = (distance in km) / (time in hrs).
For the second rate, the answer from the first calculation rate can then be converted to km / s by applying the conversion factor for 1/hr to 1/s, which is (1 hr) / (3600 s).
Analogously, the distance in km can be converted to mi by using the correct ratio for mi / km. Note that the time is given in the question as 3 days. This can be converted to hours by (24 hr) / (1 day).
Thus, the first calculation is r1 (km/hr) = (distance to the Moon in km) / (3 days * (24 hr / 1 day)).
The second rate is given by r2 (km/s) = r1 (km/hr) * (1 hr / 3600 s).
I will leave the number crunching and expression for the third set of units as an exercise for readers.
Click Here to return to the search form.
Copyright © 2020 The Regents of the University of California,
All Rights Reserved.